ADC Guide, Part 11: ADC Noise – 2, SINAD, ENoB

For convenience here are pdfs of part 10 and part 11 of the series dealing with ADC noise issues.

In the previous part of this series, we discussed about noise basics and how they affect an ADC’s output. We will continue this discussion about noise and cover Signal-to-Noise and Distortion ratio and ENoB, all commonly used specifications of an ADC.

Peak-to-peak noise is important for a very limited set of applications where the accuracy of analog to digital conversion is of utmost importance. One such example is precise weighing scales where the ADC has to measure very small analog voltages extremely accurately.

For most of the general applications of an ADC, RMS noise is the parameter considered as the measure for DC noise performance of the ADC. It is apparent in Figure 3 from the previous part of this series that the typical distribution of a grounded input histogram approximately assumes the shape of a Gaussian curve. This Gaussian curve is marked in red in Figure 3. The difference between the actual distribution and perfect Gaussian arises from the DNL of the ADC. As we have already seen in part 5 of this series, if DNL is more than -1 LSB, missing codes can result which will make this distribution go far off from an ideal Gaussian.

We can compute the RMS noise by statistical methods. As a rule of thumb, peak-to-peak noise is around 6 to 8 times the RMS noise of the ADC, assuming an approximate Gaussian distribution. RMS noise can be expressed in terms of number of counts or number of LSBs, similar to peak-to-peak noise.

The Signal-to-Noise Ratio (SNR) is the parameter of an ADC which accounts for the noise in the ADC. As it was derived in the first part of this series, the SNR of an ideal ADC is given by equation (4) below:

Click on image to enlarge.

The SNR of an ideal ADC is also known as signal-to-quantization noise ratio (SQNR) for obvious reasons.

For a practical ADC, the signal-to-noise ratio is always less than the SNR value of an ideal ADC of the same resolution due to added noise from the noise sources mentioned previously. The SNR for a practical ADC can be calculated from the FFT of the output of the ADC. It depends upon the power of the fundamental signal and noise. The noise power can be estimated by removing the power of fundamental and harmonic components from the total signal power. The RMS noise voltage is marked as vnoise in Figure 1. Therefore, the SNR of practical ADC is given by equation (5) as below:

Click on image to enlarge.

Although we do not consider the power content of the harmonics frequencies when calculating the SNR of an ADC, harmonics are in fact equally important when selecting an ADC for a particular application. ‘THD+N’ is the parameter which adds up the effect of noise and harmonics. It is defined as the power of harmonics and noise with respect to power of fundamental frequency component and is given by equation (6) below:

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